Keishi Kawabata

Directional stability radius: a stability analysis tool for uncertain polynomial systems

Coefficients of characteristic polynomials for stable parametrically uncertain systems are allowed to perturb to some extent for stability. Stability radius is a useful tool to assess the allowance of the stability for the systems. To enhance its usefulness, we modify stability radius so that it takes into account of given restricted perturbations, which we call directional stability radius. For an application, we show shifted-Hurwitz stability conditions and a stability analysis method for interval polynomial systems using the directional stability radii.

A Solution Method for Pole Placement and Stability Radius Enlargement Problem

This paper presents a robust controller design method for linear time-invariant SISO systems based on an optimization approach. The task is to enlarge real stability radius to counter plant parameter perturbations by using extra degree of freedom of the controller parameters in the pole placement scheme. The formula for the real stability radius is known as an infimum of a certain function and that makes its gradients discontinuous. It is shown that by some manipulations, the considered problem can be converted to a nonlinear optimization problem, to which a gradient-based optimization method becomes applicable. The case of complex stability radius is also considered, which is less sharp as a robust stability index than the real counterpart, but has a much simpler form. Numerical examples for both cases are presented to show that they actually work, and some comparisons are discussed, leading to a suggestion on the effective uses of these two stability radius computation methods.

Stability Analysis for Affine Linear Uncertain Polynomial Systems via Directional Stability Radius

Abstract Directional stability radius is used for stability analysis of polytopic uncertain structure. It is capable of checking stability of some polynomials at one time. The tool was originally formulated to treat interval polynomial systems. A main purpose of this paper is applying the directional stability radius to affine linear uncertain polynomial systems, which have a more general uncertain structure. It is shown that a modification of the formulation enables to extend the stability analysis for the systems.

Directional stability radius-a stability analysis tool for uncertain polynomial systems

Coefficients of characteristic polynomials for parametrically uncertain systems are allowed to perturb to some extent. Stability radius is a useful tool to analyze the stability for the systems. To enhance its usefulness, we modify stability radius so that it takes into account of given restricted perturbations, which we call directional stability radius. For an application, we show shifted-Hurwitz stability conditions and an analysis method for interval polynomial systems using the directional stability radii.